Analysis Sparse Priors Several works [1]}, [2]}, [3]}, [4]} have considered the \(\ell _1\) -regularized analysis/synthesis sparse recovery problems owing to its convexity. In order to solve the CS problem in the context of recovering natural images, optimization based techniques assumed that the input images are sparse in a fixed transform domain such as the discrete cosine transform (DCT), wavelet domain [5]}, gradient-domain [6]}, etc. Denoising based AMP (D-AMP) [7]}, etc. ensures good recovery for natural images. Most methods exploit structured sparsity of the data as an image prior and solve the problem iteratively [8]}, [6]}, [7]}, [11]}. All iterative sparse recovery methods require hundreds of iterations to solve Eq. (REF ), which inevitably gives rise to high computational overhead thus restricting the application of CS. In addition, the analysis operator or the hyperparameters such as learning rate and regularization parameter are usually hand-crafted.
